Modeling facies is a crucial step of reservoir modeling as it conditions how the petrophysical properties will be distributed afterwards. Geologists and modelers should work together on the different aspects of this modeling.

The main depositional information should be captured in the internal geometry of the 3D grid. Were the rocks deposited parallel to the base of the geological unit? parallel to the top maybe? Shall we go deeper and take into account some more complex trends identified by dipmeter data or by seismic interpretation? As explained in the section 2.3, the internal geometry of the 3D grid will have a huge impact on how the facies will be distributed. For this reason, the geometry of the 3D grid must be built with care.

Once the 3D grid is built, geostatistical techniques will likely be the tools of choice for distributing the facies data. The third paper of this series explained the fundamentals behind these techniques (see the April issue of the Reservoir). As explained in the previous paper, the most common techniques for facies modeling are indicator kriging and indicator simulation. These techniques use statistics and variograms as input. They can also take into account some secondary variable which give some extra information on how the facies proportions should vary from place to place in 3D. These secondary variables are an efficient way for geologists and modelers to capture trends in facies.

Facies proportion maps, such as the one described in the first section (Figure 4), are an example of such secondary variables. These maps will guide geostatistical algorithms in terms of how the proportions of the different facies should vary aerially. On the other hand, Vertical Proportion Curves (VPCs) detail how the facies proportions vary vertically in the reservoir. VPCs are described below. VPCs and facies proportions maps are complementary. They can be combined into a 3D cube of facies probabilities. In such a cube, each cell of the grid will be assigned with the local probability of having each given facies. At last, multiple cubes can be combined together into a single cube. Some input probability cubes might be coming from well analysis while others might be coming from seismic analysis.

How VPCs are created and stored is described here through an example (Figure 2 to Figure 12).

The wells used to create the sand probability map (Figure 1) are hereafter used to populate facies in a 3D grid using indicator simulation (Figure 2). The reservoir is a box with flat top and bottom horizons. The 3D grid is made with a horizontal layering and cell sizes of 100m*100m horizontally and 2m vertically. The concept of having a large channel North-South is used here as well. It means that, in the same way that the sand proportion map was made in two separate zones (plain and channel), the geostatistics in the 3D grid will be applied in each zone individually. Instead of using the sand proportion map, the vertical distribution of the facies is looked at and stored in VPCs.

A VPC is represented as a two-dimensional plot (Figure 3). The vertical axis represents the different horizontal layers in the 3D-grid (the different K layers – see Figure 2). For example, the top line (Figure 3, circle 1) represent the first K layer (K=1). In this specific 3D grid, the K layers are increasing from top to bottom, so the layer K=1 represents the upper two meters of the reservoir. For each K layer, the VPC captures the proportion of the different facies in that layer and this is stored in the horizontal axis of the VPC. In this VPC, the layer K=1 has about 70% of shale in average. This number is computed by looking for all the wells crossing the layer K=1 and then checking how many of them have sampled shale and sand at this depth.

In this reservoir, the proportion of shale does vary with depth. For example, from K=10 to K=15 (Figure 3, circle 2), we find about 40% of shale, while from K=15 to K=25, the proportion of shale progressively increases to 70-80% (Figure 3, circle 3). This is to compare with the global proportion of shale of 60% (Figure 3, dashed red line) which might give a false sense that one finds about 60% of shale at every depth in the reservoir.

This VPC is a global VPC as it is computed using all the data in the reservoir. Local VPCs can also be computed to check if the VPC won’t change from one side of the model to the other. Typically, one would first compute a global VPC, then split the reservoir aerially into a few blocks of same size and compute local VPCs at this scale. If each block still contains enough well data, the reservoir is split into even finer blocks. The process continues until the blocks are too small to contain enough (or any) well data. The process also stops once it is shown that the VPC are now homogeneous (splitting one more time doesn’t make any new variations to appear).

Without going to multiple levels of local VPCs, it is also useful to check if the reservoir is not split into several major zones of different deposition history. In our case, we have two such zones: the plain and the channel. When computing a VPC for each zone, one can see that they are quite different (Figure 7). The VPC in the channel shows a lot of sand at all depths (Figure 7A), while the VPC in the plain shows a lot of shale everywhere (Figure 7B). Because of this, the global VPC should not be used and we need to consider these two VPCs as input for our geostatistics.

VPCs are basically nothing more than statistics, but computed at each K layer. As such, we find the same problem with VPCs than with computing any global statistics: the value of a VPC in a given K layer can’t be trusted if this K layer is not crossed by enough well data point. The statistics in such K layers are undersampled. This appears in the VPC of the channel as the facies proportions tend to “jump” from one value to another from K layer to K layer. In comparison, the vertical changes are much “smoother” in the VPC for the plain. 6 wells are in the channel area while 13 are crossing the plain area. As a result, the VPC for the plain can be trusted more than the one for the channel.

Based on this analysis, facies are modeled in the channel by indicator simulation without VPC – we decide to ignore the VPC there. For the plain, two approaches are tested, to illustrate the impact of using a VPC. In a first model, the facies are modeled in the plain by indicator simulation without VPC (Figure 4). In a second model, the facies are modeled with VPC (Figure 5). Lastly, the VPC in the plain of each of these two distributions is computed (Figure 6). Until now, we computed VPCs from the well data as part of our data analysis and our desire to feed the geostatistical algorithms with some proper input. But it’s also possible to use VPCs to check how the facies ended up being distributed in a given model. Such VPCs are computed from all the populated cells and for us, it’s a way of checking that the modeling did (or did not) respect the input VPC.

In both models, the facies are distributed the same way in the channel area (Figure 4 vs Figure 5). This is normal as, in both cases, we used the same parameters for the indicator simulation without VPC. On the contrary, and as expected, the facies are distributed differently in the plain area. Visually, it seems that the sand is distributed vertically in a more homogeneous way in the model computed without VPC (Figure 5) than in the one using VPC as input (Figure 4). The VPCs from the two models confirm this impression. The VPC of the model computed with secondary variable is very similar to the input VPC (Figure 6A vs Figure 7B). In the meantime, the VPC of the model computed without secondary variable is not as close (Figure 6A vs Figure 7B). In both models, we have 80% of shale in the plain (this was the input global proportion). But in the model computed without VPC, at each depth, we are closer to this average 80% of shale than what the VPC from the wells was showing. This test shows that even in a reservoir like this one, where many wells are available, using VPCs ensure that we respect the general geological organization of the facies better. VPCs give a better geological control to us by removing some mathematical freedom to the algorithm as to where to distribute the facies.

Geomodelers should be a lead when analysing, cleaning and selecting VPCs ; but in this process, geologist’s input is crucial to make sure that the final product looks geologically right. The same can be said for creating facies proportion maps.